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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (6): 9-17.doi: 10.6040/j.issn.1671-9352.0.2022.260

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概率q阶犹豫模糊TODIM方法及其应用

周宇1,2,3(),周礼刚1,2,3,*(),林志超2,3,徐鑫2,3   

  1. 1. 安徽大学大数据与统计学院，安徽 合肥 230601
    2. 安徽大学数学科学学院，安徽 合肥 230601
    3. 安徽大学应用数学中心，安徽 合肥 230601
  • 收稿日期:2022-04-09 出版日期:2023-06-20 发布日期:2023-05-23
  • 通讯作者: 周礼刚 E-mail:1439552596@qq.com;shuiqiaozlg@126.com
  • 作者简介:周宇(1997—), 男, 硕士研究生, 研究方向为统计预测和决策. E-mail: 1439552596@qq.com
  • 基金资助:
    国家自然科学基金资助项目(62276146);国家自然科学基金资助项目(72171002);国家自然科学基金资助项目(71771001);安徽省自然科学基金杰出青年基金资助项目(1908085J03);安徽省学术和技术带头人及后备人选资助项目(2018H179);安徽省高校学科(专业)拔尖人才学术资助项目(gxbjZD2020056)

Probabilistic q-rung hesitant fuzzy TODIM method and its application

Yu ZHOU1,2,3(),Ligang ZHOU1,2,3,*(),Zhichao LIN2,3,Xin XU2,3   

  1. 1. School of Big Data and Statistics, Anhui University, Hefei 230601, Anhui, China
    2. School of Mathematical Sciences, AnhuiUniversity, Hefei 230601, Anhui, China
    3. Anhui Center for Applied Mathematics, Anhui University, Hefei 230601, Anhui, China
  • Received:2022-04-09 Online:2023-06-20 Published:2023-05-23
  • Contact: Ligang ZHOU E-mail:1439552596@qq.com;shuiqiaozlg@126.com

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摘要：

为了度量概率q阶犹豫模糊信息之间的差异, 基于得分函数和综合犹豫度提出一种概率q阶犹豫模糊距离测度, 并研究其性质。进而, 基于概率q阶犹豫模糊距离测度, 提出一种概率q阶犹豫模糊交互式多准则决策(TOmada de decisão interative multicritério, TODIM)方法。最后通过实例说明所提出的TODIM方法的合理性和有效性, 并进行灵敏度分析。

关键词: 概率q阶犹豫模糊集, 距离测度, TODIM, 多属性决策

Abstract:

To measure differences in probabilistic q-rung hesitant fuzzy information, a novel measure of the probabilistic q-rung hesitant fuzzy distance is proposed based on the score function and overall hesitancy. The properties of this measure are discussed. A probabilistic q-rung hesitant fuzzy TODIM method is proposed based on the new distance measure. Finally, a practical example is presented to illustrate the reasonableness and effectiveness of the proposed method, and a sensitivity analysis is performed.

Key words: probabilistic q-rung hesitant fuzzy set, distance measure, TODIM, multi-attribute decision-making

中图分类号: 

  • O159

表1

概率$q$阶犹豫模糊决策矩阵$\widetilde{\boldsymbol{R}}=\left(\tilde{r}_{i j}\right)_{5 \times 4}$"

C1 C2 C3 C4
X1 {〈0.5, 0.2〉(0.6),
〈0.6, 0.3〉(0.4)}		 {〈0.4, 0.3〉(1)} {〈0.2, 0.5〉(0.3),
〈0.3, 0.6〉(0.7)}		 {〈0.6, 0.1〉(0.5),
〈0.7, 0.2〉(0.5)}
X2 {〈0.3, 0.3〉(0.3),
〈0.5, 0.3〉(0.4),
〈0.5, 0.4〉(0.3)}		 {〈0.5, 0.1〉(0.3),
〈0.6, 0.2〉(0.5),
〈0.7, 0.1〉(0.2)}		 {〈0.4, 0.2〉(0.5),
〈0.5, 0.2〉(0.3),
〈0.6, 0.3〉(0.2)}		 {〈0.5, 0.2〉(0.6)
〈0.7, 0.2〉(0.4)}
X3 {〈0.3, 0.2〉(0.4),
〈0.7, 0.2〉(0.6)}		 {〈0.6, 0.2〉(0.5),
〈0.7, 0.2〉(0.5)}		 {〈0.1, 0.3〉(0.2),
〈0.2, 0.5〉(0.2),
〈0.3, 0.6〉(0.6)}		 {〈0.2, 0.4〉(0.6),
〈0.3, 0.6〉(0.4)}
X4 {〈0.3, 0.2〉(0.4),
〈0.4, 0.3〉(0.3),
〈0.5, 0.3〉(0.3)}		 {〈0.4, 0.1〉(0.6),
〈0.6, 0.3〉(0.4)}		 {〈0.3, 0.3〉(0.4),
〈0.4, 0.4〉(0.6)}		 {〈0.5, 0.1〉(0.6),
〈0.6, 0.2〉(0.4)}
X5 {〈0.3, 0.1〉(0.7),
〈0.5, 0.2〉(0.3)}		 {〈0.4, 0.1〉(0.6),
〈0.6, 0.3〉(0.4)}		 {〈0.3, 0.5〉(0.4),
〈0.4, 0.2〉(0.2),
〈0.5, 0.2〉(0.4)}		 {〈0.5, 0.2〉(1)}

表2

规范化决策矩阵R =(rij)5×4"

C1 C2 C3 C4
X1 {〈0.5, 0.2〉(0.6),
〈0.5, 0.2〉(0),
〈0.6, 0.3〉(0.4)}		 {〈0.4, 0.3〉(0),
〈0.4, 0.3〉(0),
〈0.4, 0.3〉(1)}		 {〈0.3, 0.6〉(0.7),
〈0.2, 0.5〉(0),
〈0.2, 0.5〉(0.3)}		 {〈0.6, 0.1〉(0.5),
〈0.6, 0.1〉(0),
〈0.7, 0.2〉(0.5)}
X2 {〈0.3, 0.3〉(0.3),
〈0.5, 0.4〉(0.3),
〈0.5, 0.3〉(0.4)}		 {〈0.5, 0.1〉(0.3),
〈0.6, 0.2〉(0.5),
〈0.7, 0.1〉(0.2)}		 {〈0.4, 0.2〉(0.5),
〈0.5, 0.2〉(0.3),
〈0.6, 0.3〉(0.2)}		 {〈0.5, 0.2〉(0.6)
〈0.5, 0.2〉(0),
〈0.7, 0.2〉(0.4)}
X3 {〈0.3, 0.2〉(0.4),
〈0.3, 0.2〉(0),
〈0.7, 0.2〉(0.6)}		 {〈0.6, 0.2〉(0.5),
〈0.6, 0.2〉(0),
〈0.7, 0.2〉(0.5)}		 {〈0.3, 0.6〉(0.6),
〈0.2, 0.5〉(0.2),
〈0.1, 0.3〉(0.2)}		 {〈0.3, 0.6〉(0.4),
〈0.2, 0.4〉(0),
〈0.2, 0.4〉(0.6)}
X4 {〈0.3, 0.2〉(0.4),
〈0.4, 0.3〉(0.3),
〈0.5, 0.3〉(0.3)}		 {〈0.4, 0.1〉(0.6),
〈0.4, 0.1〉(0),
〈0.6, 0.3〉(0.4)}		 {〈0.3, 0.3〉(0.4),
〈0.3, 0.3〉(0),
〈0.4, 0.4〉(0.6)}		 {〈0.5, 0.1〉(0.6),
〈0.5, 0.1〉(0),
〈0.6, 0.2〉(0.4)}
X5 {〈0.3, 0.1〉(0.7),
〈0.3, 0.1〉(0),
〈0.5, 0.2〉(0.3)}		 {〈0.4, 0.1〉(0.6),
〈0.4, 0.1〉(0),
〈0.6, 0.3〉(0.4)}		 {〈0.3, 0.5〉(0.4),
〈0.4, 0.2〉(0.2),
〈0.5, 0.2〉(0.4)}		 {〈0.5, 0.2〉(0),
〈0.5, 0.2〉(0),
〈0.5, 0.2〉(1)}

图1

ξi关于不同参数值q的变化图"

图2

ξi关于不同参数值θ的变化图"

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